[Note 15] (p, 38). The term "inertial system" was originally not associated with the system, which Neumann attached to the hypothetical body
. Nowadays it is generally understood to signify a rectilinear system of co-ordinates, relatively to which a point-mass, which is only subject to its own inertia, moves uniformly in a straight line. Whereas C. Neumann only invented the body
, as an absolutely hypothetical configuration, in order to be able to formulate the law of inertia, later researches, especially those of Lange, tended to show that, on the basis of rigorous kinematical considerations, a co-ordinate system could be derived, which would possess the properties of such an inertial system. However, as C. Neumann and J. Petzoldt have demonstrated, these developments contain faulty assumptions, and give the law of inertia no firmer basis than the body
introduced by Neumann.
Such an inertial system is determined by the straight lines which connect three point-masses infinitely distant from one another (and thus unable to exert a mutual influence upon one another) and which are not subject to any other forces. This definition makes it evident why no inertial system will be discoverable in nature, and why, consequently, the law of inertia will never be able to be formulated so as to satisfy the physicist. References:—
C. Neumann. "Ueber die Prinzipien der Galilei-Newtonschen Theorie," Leipzig, 1870.
L. Lange. "Berichte der Kgl. Sächs. Ges. d. Wissenschaften. Math.-phil. Klasse," 1885.